There are three possibilities for the position of a new gene c with regard to two known genes a and b that are separated by map distance p: c is 1) to the left of both a and b; 2) to the right of both a and b; 3) between a and b.

Without recombination we expect the following phenotypes (I'll call them the parental - as opposed to the recombinant - phenotypes) in the progeny of ab/c animals: AB, C, & WT.

Recombinant phenotypes could theoretically be A, B, BC, AC, or ABC. However, if recombination is rare because p is small, the only commonly occurring recombinant progeny will be animals with one recombinant chromosome and one parental chromosome. These
animals will have either the A or the B phenotype. The recombinant chromosome would result from a recombination between a and b and the parental chromosome would be the ab chromosome.

If we take these A or B recombinant animals and look at their progeny, we will be able to determine whether the recombinant chromosome had the c mutation.

For our three possibilities (and just looking at phenotypes produced with no recombination):

1) A animals produce A and AB progeny

B animals produce B, AB, and BC progeny

2) A animals produce A, AB, and AC progeny

B animals produce B and AB progeny

3) Some A animals produce A, AB, and AC progeny, some just A and AB. Some B animals produce B, AB, and BC progeny, some just B and AB.

These results give the following rule: If c is to the right of a and b, then it associates with a; if c is to the left, it associates with b; if c is between a and b, it associates some of the time with both.

The position of c between a and b can be determined by counting the recombinant chromosomes and knowing the map distance p between a and b. For example, suppose that p is 2.0 and the following results are found:

13 A recombinants produce A and AB progeny

3 A recombinants produce A, AB, and AC progeny

9 B recombinants produce B and AB progeny

15 B recombinants produce B, AB, and BC progeny

These data indicate that if a is at position 0.0 (an arbitrary position) and b is at 2.0, then c is at 0.6.